簡約 (2/5)^9*(3/7)^9

解

簡約

(\frac{2}{5})^{9} \cdot (\frac{3}{7})^{9}

\frac{10077696}{7.88156 E 13}

十進法表記

1.27864 E - 7

解答ステップ

(\frac{2}{5})^{9} (\frac{3}{7})^{9}

(\frac{2}{5})^{9} = \frac{512}{1953125}

= \frac{512}{1953125} (\frac{3}{7})^{9}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{3}{7})^{9} = \frac{3 ^{9}}{7 ^{9}}

= \frac{512}{1953125} \cdot \frac{3 ^{9}}{7 ^{9}}

3^{9} = 19683

= \frac{512}{1953125} \cdot \frac{19683}{7 ^{9}}

7^{9} = 40353607

= \frac{512}{1953125} \cdot \frac{19683}{40353607}

\frac{512}{1953125} \cdot \frac{19683}{40353607} = \frac{10077696}{7.88156 E 13}

= \frac{10077696}{7.88156 E 13}